Force at cut toroid faces

[Geoff J]

I need to calculate the force at the faces of a cut toroidal core using a tensioning strap.

If a toroid is cut perfectly in half giving 2 equal semicircular arches with flat faces and they are placed as shown with an applied force of 100N the force at each faces logically equals 50N.

If the force of 100N is applied by a inline cable tie or tensioning strap around the circumference what is the force at each core face ?

In my opinion the tension on the strap will be 100N around the complete circumference so the force at each gap will be 100N or is this a flawed premise ?

 

[rb1957]

not really getting your "toroidal" reference.

in your RH sketch, you have a circle loaded tangentially. So I'd say that (locally) the section would react as ...
1) the 100N load is applied through the center, and
2) a torque of 100R is applied.

1) is the same as your LH sketch, the torque is reacted by a shear flow around the circle (= T/(2*[A]) = 100*R/(2*pi*R^2) = 50/(pi*R) N/mm

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Geoff J]

Rb, thanks for your response.

It is a toroidal magnetic core 31*25*5mm cut precisely in half to give 2 semicircular cores. The core faces have to be ultra flat & forced together with perfect alignment in all planes.

We are trying to achieve a force at each core face of around 50N and have designed a custom strap ( like a cable tie ) with a hooked clasp which integrates with a latch so the tension is applied by clicking the latch into place.

The tension is adjusted by moving the clasp in 1mm increments using the cable tie action.

The action of the strap also cures all alignment problems.

We have tested the strength of the strap linearly but to check the results we are trying to estimate that if we are achieving 50N at each core face, what is the required tension on the strap and is it within its linear rating.

More tests may be required.